types of efficiencies — Tarik Yildirim

Nature seems to be optimizing at several levels. For example,

1) Particles minimize energy consumption.
2) Organisms minimize calorific consumption.
3) Companies minimize costs.

But why?

3) Shareholders press for higher returns. Cutting costs increase competitiveness and chances of survival.
2) Managing net calorific intake increases the possibility of successful reproduction by increasing resistance to environmental shocks.
1) No idea. In biology and economics, efficiency emerges out of the system constraints. However, in physics, it is just part of the system constraints.

There may be selectionary evolutionary pressures at work in physics too.

The organisms that we see around are good at minimizing calorific costs. Why? Because if they were not, they would not have survived until now and therefore would not be observable by us. Particles we see around are good at minimizing energy costs. Why? Because if they were not, the resulting physics would not exhibit the properties that render our presence possible, and therefore would not be observable by us. (See: Anthropic Principle and Cosmological Natural Selection)

Note that the discovery of such "environmental" constraints for physics may be outside our experimental reach. Let's just keep this discourse quiet so that we will not raise Karl Popper from his grave with our non-falsifiable conjectures.

Wittgenstein would have also shuddered at the thought of physics taking place in some environment. Physics is by definition all encompassing. Regularities in physics are not by-product of anything else. They can only be self-induced. In particular, they can not arise due to a competition in a greater realm.

Although it is silly, let's imagine that there indeed is a "greater realm". Then you can iterate the same question: "Why are the rules of competition between different physics the way they are? Is this set of rules also a result of some competition?" To answer such questions, you will inevitably end up conjuring competitions inside competitions inside competitions... realms inside realms inside realms... Ad infinitum!

In short, our speculation does not even make logical sense. Hence it would have been crossed out by Wittgenstein before it even reaches Popper.

In fact, calling the behaviour of a particle "efficient" is misleading. A particle is not making calculations within the theoretical framework we subscribe to nature. It is just being a particle. That is all. What we are observing is not efficiency but simply regularity, and our theoretical framework makes this regularity look like efficiency.

Update (August 2010)

I have just discovered that the questions posed above have first been considered in the 18th century:

In 1748 Maupertuis showed that Newton's laws of motion could be derived by the application of a teleological principle. It is possible to define a mathematical quantity, the action, which involves the product of mass, velocity, and distance travelled by bodies. Maupertuis's Principle, which we now call the Principle of Least Action, was that

If there occurs some change in Nature, the amount of action necessary for this change must be as small as possible.

This elegant idea turns out to be equivalent to the Newtonian laws of motion (although it is more powerful in the sense that it can be used to derive the equations of motion in other areas of physics once the appropriate action is identified.) But, unlike the formulation of Newton, it is teleological. It says that, of all the paths that could be taken by a body moving from A to B, it actually takes that path for which the associated action is a minimum. This path is therefore determined by both the initial and the final states. Maupertuis attached great metaphysical significance to this result, regarding it as a "proof of existence of Him who governs the world". Formerly, arguments of the sort that we lived in the "best of all possible worlds" were open to the objection that we did not know any other worlds with which to draw such a comparison, but Maupertuis claimed that the other worlds were those in which motion occurred with non-minimal action. Our world was optimal in this well-defined sense, and moreover there existed a teleological aspect to the laws of Nature (in fact, some nineteenth-century commentators interpreted the existence of fossils as relics of the still-born worlds of non-minimal action.)

Barrow - Universe That Discovered Itself (Pages 88-89)